Probability Distribution of X, Y & N(i): Questions & Answers

In summary, the conversation discusses various distributions in probability, such as the number of balls in an urn, number of throws needed to get a pair of sixes, duration of batteries, and the throw number when a specific number is rolled on a dice for the first time. The distributions mentioned include uniform, geometric, and exponential with different parameters. The speaker also mentions difficulties in determining the distributions without proper resources.
  • #1
JohanL
158
0
I have some simple questions about distributions in probability.
what are the distributions for X, Y and N(i) in these cases:

1. You have k urns and n balls. X is the number of balls in one urn.

2. You throw two dices until you get a pair of sixes. X is the number of throws.

3. You have three batteris A,B and C. There durations (? how long they last. I am from sweden) have exponential distributions with DIFFERENT parameters. If you first use A and B in a lamp what is the distribution for X, the time the
lamp works. Then you replace the nonworking battery with battery C. What is the distribution for Y, the time the lamp works after the exchange.

4. You throw one dice over and over again. Let N(i) be the throw when you get i for the first time. What is the distribution for N(i).

Thank you.

I have no problem to do the calculations when i know the distributions. The hard point for me is to figure out the distributions...my book isn't so good.
 
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  • #2
1. not enough information. you presumably uniformly distributed.

2 is geometric

3. scratch 3, that was wrong.

4. geometric again.
 
Last edited:
  • #3
Thx
But what's wrong with 3...its a problem from the book.
 
  • #4
my answer was wrong, not the question.
 

1. What is a probability distribution?

A probability distribution is a mathematical function that describes the likelihood of each possible outcome of a random variable. It shows how probabilities are distributed across all possible values of the variable, and is often represented by a graph or table.

2. What is the difference between X, Y, and N(i) in probability distributions?

X, Y, and N(i) are all different types of random variables. X and Y are discrete random variables, meaning they can only take on certain values. N(i) is a continuous random variable, meaning it can take on any value within a certain range. In probability distributions, X and Y are typically used to represent the outcomes of events, while N(i) is used to represent a continuous process.

3. How is the probability of a specific outcome calculated in a probability distribution?

The probability of a specific outcome is calculated by finding the area under the curve of the probability distribution function for that particular outcome. This can be done using calculus or by using a probability table or chart.

4. What is the difference between a discrete and continuous probability distribution?

A discrete probability distribution is used for random variables that can only take on specific values, while a continuous probability distribution is used for random variables that can take on any value within a certain range. Discrete distributions are represented by a bar graph or probability table, while continuous distributions are represented by a smooth curve.

5. How is a probability distribution related to the concept of expected value?

The expected value of a probability distribution is the weighted average of all possible outcomes, where the weights are the probabilities of each outcome. It represents the average outcome over a large number of trials. The expected value is often used to make decisions or predictions in real-world scenarios.

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